THE EFFECTIVENESS OF DAMATH IN ENHANCING THE LEARNING PROCESS OF FOUR FUNDAMENTAL OPERATIONS ON WHOLE NUMBERS Marilyn Morales- Obod, Ed. D. Our Lady of Fatima University, Philippines Presented in Pullman Hotel Kuching, Sarawak Malaysia October 22, 2013
WHAT IS DAMATH? Dama DAMATH Mathematics
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Why teaching tool for high school mathematics only? How about elementary school mathematics?
HISTORY OF DAMATH Province of Sorsogon, Bicol Region, Philippines encountered problems in teaching math using traditional teaching methods public school teacher student investigatory project Dama de Numero overhauled the game introduced it to his class, enjoyed playing. Jesus L. Huenda,
DAMATH GREW IN POPULARITY!!!!!!! 1 st Damath tournament was held in Sorsogon, Phil., 1980 Huenda received a gold medallion from the late President Ferdinand Marcos for his contributions in the field of teaching mathematics, 1981
DAMATH reached its peak popularity in the 1990s It made the rounds of several mathematics education conventions all over the world. 10th Conference of the Mathematical Association of Western Australia UNESCO-ICT4E conference, Thailand SEAMEO RECSAM/SEAMEC conference, Malaysia APEC Learning Community Builders (ALCoB) conference, Korea
Memorandum enacted by the Department of Education encouraging public and private schools to integrate DAMATH in the teaching of Mathematics Public and Private Schools conducted their own version of DAMATH Competitions both in elementary and secondary levels
THE GAME
THE GAME OF CHESS
THE GAME OF DAMA Dama uses the checkers board or chess board
TO UNDERSTAND DAMATH MEANINGFULLY, WE HAVE TO UNDERSTAND FIRST HOW TO PLAY DAMA.
DAMA Countries around the world have their own versions of the game called "checkers", a name which gets its roots from North America. In the Philippines and in Armenia, the game is called dama.
PLAYING DAMA The game is played by two people, each with 12 pieces of pitsas or chips made from bamboo, stones, or bottle caps. Player position the 12 pieces of chips" on the end points of the diagram. They move from point to point, and like chess, the game ends once the opponents chips are captured.
In some parts of the Philippines, the game is played using a chess board and its pieces. The pawns, knights, and rooks are usually used at the start, while the kings, queens, and bishop are used when a player reached the "dama". The "dama stage" is reached when a player gets his piece to the last row of the board.
The chips can only move diagonally along the intersection of lines or squares in chessboards Chips cannot eat or capture backwards. Chips that have reached the "dama stage" can move from row to row diagonally.
ILLUSTRATE HOW TO PLAY DAMA dama dama dama dama dama dama dama dama
SAMPLE DAMATH BOARD
DAMATH BOARD The Damath board, similar to a chess board, consists of 8 x 8 squares alternating in black and white. On the white squares are the four basic Mathematical operations--addition, subtraction, multiplication and division.
DAMATH GAME
ORIGINAL RULES IN PLAYING DAMATH- As the name implies, the game is essentially the same as dama but with an added math twist: in order to win in Damath a player must score the most points which are earned by eating the opponent's pieces. the player must solve the mathematical operation on the square in which the opponents piece is currently standing.
The answer to that mathematical operation is the amount of points that the player will receive when s/he does eat the opponent's piece. players have to do mathematical computation whenever they capture an opponent s chip. The game will go on until all pieces belonging to a player have been eaten and the scores computed.
EXAMPLE if the piece marked 1 eats the piece marked 3, with 3 standing on a multiplication square, the player must first solve the operation (1 x 3 = 3) and will get three points.
Because of the need to solve operations, players must list down all moves during the game so the moves can be reviewed, especially by the judges in a tournament setting. The two players alternately take turns in moving a chip (pass is not allowed) Each player is allotted one minute per move including the computing of the move and the corresponding score in the score sheet.
GAMES FOR DAMATHS COMPETITIONS: ELEMENTARY LEVEL Levels Grades - Contents Level 1 Grades I II - Counting Numbers Level 2 Grades III IV - Whole Numbers Level 3 Grades V VI - Positive Fractions
HIGH SCHOOL Level 4 First Year - Level 5 Second Year - Level 6 Third Year - Level 7 Fourth Year - Integers Signed Fractions Radical Damath Polynomial Damath
OBJECTIVES Integrate the Filipino checkerboard game of dama into the teaching of mathematical concepts and skills Encourage the utilization of recycled materials in preparing damath board and chips (set for the classroom use only) Analyze damath as possible subject of mathematics investigations. Enhance wholesome interpersonal relations among players Promote mathematical consciousness among family members in particular and the community in general through mathematics club s community outreach damath competitions Promote awareness of girls in mathematics (as king is to the game of chess, so dama (for lady) is to damath
DAMATH GAME modified by Dr. Marilyn Morales-Obod presented in icotlg 2013 Pullman Hotel Kuching, Sarawak, Malaysia October 22, 2013
DAMATH BASIC GAME - WHOLE NUMBERS 7 6 5 4 3 2 1 0 0 x dama - dama dama + dama 0 1 x + - 1 2 + - x 2 3 x - + 3 4 - x + 4 5 + - x 5 6 + x + 6 7 dama - dama dama x dama + 7 7 6 5 4 3 2 1 0
MODIFIED DAMATH GAME- DECIMALS 7.6 5.4 3.2 1 0 0 x dama - dama dama + dama 0.1 x + - 1 2 + - x.2.3 x - + 3 4 - x +.4.5 + - x 5 6 + x +.6.7 dama - dama dama x dama + 7.7 6.5 4.3 2.1 0
MODIFIED DAMATH GAME- INTEGERS 7-6 5-4 3-2 1 0 0 x dama - dama dama + dama 0-1 x + - 1 2 + - x -2-3 x - + 3 4 - x + -4-5 + - x 5 6 + x + -6-7 dama - dama dama x dama + 7-7 6-5 4-3 2-1 0
SIMPLIFIED RULES IN PLAYING DAMATH GAME The game is played by two students, each with 12 pieces of chips Player positions the 12 pieces of chips" on the end points of the diagram The two players alternately take turns in moving a chip (pass is not allowed). Moving a chip means sliding it diagonally in the forward direction only except when taking an opponent's chip or if a 'dama' chip takes an opponent's chip. A player who touches a chip ('touch move') is required to move unless it is not possible to do so After each 'move', a player has to form the equation using the numbers and the operation involved Toss a coin to determine which player will have the first 'move'. In the Philippines, children start the game with bato - bato pick
EXAMPLE If the possible move of the chip landed on the space with + sign and it is the intersection of nos. 3 and 2 The equation formed is 3 +2 = 5 For this particular move, the score is 5 If landed on x sign, the equation would be 3 x 2 = 6, and the score is 6 The player has to record this equation in a score sheet (only one score sheet will be used by the two players).
SIMPLIFIED RULES IN PLAYING DAMATH GAME In case the chip landed on sign and the numbers involved are not divisible, + or x may be used ; whichever will give the higher score since the objective of the game is to get the higher score in order to win
SIMPLIFIED RULES IN PLAYING DAMATH GAME If the possible move of the chip landed on the space with sign and it is the intersection of nos. 4 and 7 For this particular move, the score is 28 the equation formed is 7 4 And since 7x 4 = 28 will give a higher answer, it may be used by the player but 7 is not divisible by 4 The player may use either, 7+4 = 11 or 7x 4 = 28
SIMPLIFIED RULES IN PLAYING DAMATH GAME Each player is allotted one minute per 'move' including the recording of the 'move' and the corresponding score in the score sheet In taking an opponent's chip, the 'taker' chip jumps over the 'taken' chip and uses any of the four operation symbols of +, -, x, and -:- where the taker chip lands Similarly, the opposing player's chip is declared 'dama' if it stops in any of the following squares: (0,7) (2,7) (4,7) (6,7) A chip is declared 'dama' if it stops in any of the following squares of the opposing player: (1,0) (3,0) (5,0) (7,0)
SIMPLIFIED RULES IN PLAYING DAMATH GAME 'dama' chip can slide diagonally forward or backward in any unoccupied square as long as no opponent's chip blocks its path could take a chip or chips whereby its corresponding sum, difference, product or quotient is doubled Similarly, if an ordinary chip takes an opponent's 'dama' chip, its score is also doubled
DAMA chips move from point to point the game ends if: an opponent's chip is 'cornered' time limit set for the game period lapsed moves are repetitive a player has no more chip to move
HOW TO SCORE/WIN Check the equations written on the score sheet The answer of each correct equation is the score for that particular move Equations with wrong answer will not get any point. Deduction for wrong answer is discouraged if it is played to reinforce the lesson but it may \be applied if the game is played during competitions The answers of the correct equations will totaled to get the final score of each player The player with the higher score wins the game
Possible Modifications The numbers put around the damath board may be changed according to the subject matter and the number literacy of the players The +, -, x, and signs may be put in any order provided NO operation sign is repeated in a row or column The chip could be in any form (e.g stone, shell, bottle caps or crown, card board cut into pieces, cover of clear books cut into pieces, and the like) depending upon the availability of materials in the locality The rules of the game may be enhanced depending upon the creativity of the teacher
LET S PLAY DAMATH